Answer:
[tex]CAB = 42[/tex]
Step-by-step explanation:
Given
[tex]CAB = 2x + 30[/tex]
[tex]DAB = 5x + 12[/tex]
Bisector: AB
Required
Find CAB
Since AB bisects CAD, then
[tex]CAB = DAB[/tex]
This is so because AB divides CAD into two equal parts which are CAB and DAB
[tex]CAB = DAB[/tex]
Substitute values for CAB and DAB
[tex]2x + 30 = 5x + 12[/tex]
Collect Like Terms
[tex]2x- 5x = 12 - 30[/tex]
[tex]-3x = -18[/tex]
Divide both sides by -3
[tex]x = 6[/tex]
To solve for CAB, we simply substitute 6 for x in [tex]CAB = 2x + 30[/tex]
[tex]CAB = 2 * 6 + 30[/tex]
[tex]CAB = 12 + 30[/tex]
[tex]CAB = 42[/tex]
